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today we have to find the area of this
inscribed Square only given thing is
this radius of the quarter Circle which
is 10 can you solve it let us label the
side of this Square as X if you see this
line of the square it also represents
the chord of the quarter Circle so we
can use a perpendicular bis sector which
will divide this chord into two equal
parts therefore this piece will be x/2
this piece is the same as the side of
the square that is X now consider this
right triangle since both of these lines
are parallel therefore this
perpendicular bis sector will also
divide this side into two equal parts
and thus both of these angles will also
be the same which will be
45° so this will be an isoceles right
triangle which means all of these angles
will be
45° now consider this part both angles
are equal therefore this side will also
be = to x / 2 all right now we will
construct a line from the center of this
quarter Circle to this vertex of the
square this line is also the radius of
the circle and thus it will be 10 great
now finally consider this right triangle
this side is X /2 this side will be x /
2 + x or 3 x / 2 and the hypotenuse is
10 so using Pythagoras Theorem we get 10
2 = x / 2 2 + 3 x / 2 2 this will be x²
over 4 + this will be 9 x² over 4 and it
will be equal to 100 this will become 1
+ 9 or 10 x^2 / 4 = 100 so 10 x² will be
400 or x² = 40 our question was to find
the area of this inscribed square and
since its side is X therefore the area
will be x square or 40 this is our
answer don't forget to put the square
units so good
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